Pre-Stressed

Let’s go back in time, to the ancient Romans, who discovered how to make and use concrete, and could even make it work under water. But the weakness of concrete in tension meant that it was only useful in masses like walls, or in compression, as in arches.

Eventually, when strong metals were available, it became possible to reinforce concrete with iron or steel rods. In 1808, for example, Richard Dodds took out a patent for reinforced concrete. In principle, the concrete could even be allowed to develop slight tension, because any cracks would be limited by the tension in the rods. The improvement of the design of the reinforcement and its coupling to the concrete required many years of development, and is a specialist subject.

These two pictures show a concrete beam bridge made by pouring concrete around steel reinforcing rods. Erosion has revealed the metal at the sides of the bridge, probably aided by corrosion of the metal. The potential of reinforced concrete was shown dramatically by Robert Maillart, who made art out of technology by recognising and following the logic of the materials.

Unless we find a reinforced concrete bridge in course of construction, it is not easy to see reinforcing in action, but here is a window that has been struck by a heavy implement. The steel wires have not prevented the window from cracking, but they have prevented the panes from falling apart. In the same way, cracks may develop in reinforced concrete, but the material holds together, though corrosion may result if moisture can reach the reinforcing bars. In a reinforced concrete structure, the shaping and placement of the bars is a subtle art.

Composite materials open up possibilities that are denied to the users of isotropic substances. Straw in bricks, Tufnol, and fibreglass are a few examples.

In 1934, Eugene Freysinnet repaired Le Havre station using stressing wires. He went on to develop the art of pre-stressed concrete to a high degree. Actually, it is not uncommon to see old buildings with metal plates and nuts on the outside, showing where rods have been passed right through to hold bulging walls.

Donnington Bridge – Oxford

It used to be a joke that something was made from string and sealing-wax. In fact a small model of a bridge could be made using sealing was, which is very brittle, and string, which can take tension. The string would have to have a high value of Young’s modulus to prevent it stretching too much. A simple model of a stressed beam can be made with a set of wooden blocks with grooves in them, and a piece of piano wire with a washer soldered at each end. The washers are placed so that when all the blocks are lined up, the washers just fit over the ends. It is easy to make a beam a metre long that you can stand on when it is supported at the ends.

The upper pictures show Donnington Bridge over the river Thames, south of Oxford. This bridge comprises a number of very flat beams, joined by deck slabs. Such a structure could not exist in concrete but for the tensioning wires, which make it into something rather like an enclosed cable-stayed bridge, with the wires sloping down from the ends towards the middle. Not only does the span conceal its structure, but also so do the very solid looking abutments, which are only walls, concealing V-legs, rather like those in the pictures of the footbridge in the second row of pictures. The difference is that Donnington bridge uses beams, whereas the footbridge has a central hinge, as well as hinges at the feet. Because of the rigidity introduced by the legs, there must be outward thrust at the foundations in the footbridge, which like an extremely non-funicular three-pinned arch.

Footbridge near Oxford

A footbridge near Oxford, on the southern ring road, using stressed concrete. The Romans of the empire built some magnificent structures, but they would marvel at this, as they would at the bridges that carry Italian autostrada across difficult terrain today.

Another concrete footbridge, in a university park.

How Pre-Stressing Works

There are three different ways of putting steel into concrete – reinforcing, pre-tensioning and post-tensioning. Reinforcing consists in placing long steel rods in the moulds before pouring the concrete. The result is a composite material like fibre-glass. Stressing goes further – the steel are tensioned to the level which ensures that the concrete will never experience any tension. By this means a concrete beam or cantilever can be made far thinner than a reinforced one. Stressing, in fact, enable concrete to do jobs that would otherwise be unthinkable.

Two of the great names in concrete are Robert Maillart, who built elegant bridges in reinforced concrete in Switzerland, and Eugene Freyssinet, who pioneered pre-stressed concrete in France. They have been followed by many other brilliant engineers. Sadly, concrete, like steel, is at the mercy of the designer, or perhaps the budget, and the word is for some people almost synonymous with ugliness. This is a great pity, because many concrete structures are extremely elegant.

A northward journey on the M1 motorway from London to Leeds and beyond will provide a wealth of bridge-watching opportunities, and also a journey in time, revealing the changes in styles and attitudes which have taken place during the last forty years.

How does pre- or post-tensioning work? The picture below gives a simplified description. So simplified, in fact that at least two important considerations have been left out. These will be discussed later.

At the top is a beam resting on the ground. The grey tint represents a stress-free condition. In the middle it is resting on two supports. Now the top is in compression and the bottom is in tension, and along the middle there is a neutral plane with little or no stress. If the beam is made of wood or steel this could be acceptable, but if it is of cast iron or concrete, the acceptable strain will be far less. Before steel came into use in the19th century, the use of cast iron presented problems, and wrought iron had to be used for tension bars in suspension bridges and trusses. There were some failures in cast iron trusses.

In the lowest diagram the three white lines represent steel wires placed under a suitable tension. Now the top of the beam is more compressed than before, shown by the bright red, while the bottom has lost all the tension. This diagram represents the case where the beam has been loaded to the point where any more load would create some tension at the bottom. In practice a design would not be pushed so far. Placing wires in these positions is far from efficient – a better solution is shown below. After all, wires near the top in the middle aren’t very useful because the concrete can resist compression without help.

Now the red is not so bright as with the parallel wires, because the beam is not being compressed unnecessarily, yet there is still no tension. In a sense, the beam is almost like an enclosed self-anchoring suspension bridge. Some early bridges by Freysinnet, for example at Esbly in France, still look very elegant. Parts of these bridges were assembled and tensioned together, and then lifted into place as complete units.

Above these diagrams it was stated that there were omissions.

If we look at these beams and imagine that near the ends they are made of very soft material, it is clear that the supports will tend to shear a thin slice off the ends. Shear stress has been ignored in these diagrams.

Furthermore, it is clear that right at the ends, nothing is trying to bend the beams. The bending moment varies smoothly along the beams, being biggest in the middle and zero at the ends. So here is a new set of diagrams, below, which takes bending moment, though not shear stress, into account, in the diagram at the bottom of the picture.

The next picture shows a piece of foam plastic that has been cut in five places with scissors to simulate the weakness of concrete in tension. It is being stressed on a work bench.

The widths of the cracks shows where the curvature, caused by the bending moment, is greatest. In the next picture we see some rubber bands, and in the third picture, the result of placing them in a longitudinal slot.

The pre-stressing provided by the rubber bands has curved the beam. The same effect, though much less pronounced, can be seen in pre-stressed concrete beams. Finally, in the picture below, we see the beam being loaded. Look very carefully at the profile of the beam. It retains the some of the pre-curve between the loads, but curves the other way around the load. Now imagine the effect of a heavy truck passing over a pre-stressed concrete beam.

It is possible to learn a lot about structures and materials using simple materials that are readily available.

Second Severn Crossing

At the Severn Bridges visitor centre you can see some examples of stressing wires as used in the approach spans. The fittings make it quite clear how the wires could be pulled by jacks and then locked into place by the conical collets. The method of gripping allows for later adjustments of the tensions if necessary.

The picture at left shows some of the 23 approach spans at the eastern end of the new Severn bridge near Severn Beach. These spans were assembled from match-cast concrete sections, one outlined in black in the picture, stressed together with wires after placement. The bridge contains about 6800 km of stressing wires.

The picture below gives a rough idea of the method of gripping a wire in a tapered ferrule.

You can find pictures of pre-stressed footbridges by clicking here.

This water tower must have stressing wires inside the concrete of the reservoir, in order to take the tension induced by the pressure of the water. The building uses reinforced concrete. The stack behind is based on a set of tubes to provide rigidity.

The diagram shows a part of the mast and boom of a sail-boat. The boom is a beam that holds the bottom of the sail, against the tension caused by the wind.

The boom is held down by a vang, the rope which is shown under the boom. Using this, the boom can be set at a required vertical position.

If the wind drops, the boom will not be pulled upwards, and will drop.

To pre-stress the beam against the vang, various arrangements are in use.

A very elegant and simple one is the BoomKicker^TM (USA patents 507082 and 6062155). It consists of parallel fibre-glass rods, which are connected to the boom and mast with a bend that produces the pre-stress.

Most structural materials have a high Young’s modulus, giving a huge change in force for a small change in length. The curved rods produce a force which varies rather weakly with the overall length, which is the requirement here.

The height of the boom can then be adjusted using only the vang.

See http://www.boomkicker.com/

Masts

The masts of a sailing craft must be strong and stiff, to withstand the variable stresses they encounter. To achieve the desired properties without excessive weight, masts are made light, and braced externally by struts and wires.

Sometimes masts will break under the often very sudden shocks that they they commonly receive.

Unlike an aeroplane or a balloon, which can largely move with the air, a boat is anchored in the water by a hull and a keel. These, of course, make sailing possible, where a balloon can only drift. Like the air, the water can inflict immense forces on a boat, which can translate into tremendous stress on fittings.

In the lower pictures we see that the masts are anchored only at the top in the fore-and-aft direction, but in between in lateral direction. This enables the mast to be much thinner laterally, and therefore much lighter.

The Pneumatic Tyre

The pneumatic tyre was a great invention. Such tyres hold up bicycles, motor-bikes, cars, buses, trucks, aircraft, and many other wheeled forms of transport.

How do they work? What keeps the rim of the wheel off the ground?

It seems that it must be connected with the air pressure, because if you let the air out, the tyre goes flat at the bottom, letting the metal rim touch the ground.

How does the air do the trick? The pressure is the same all round the wheel, so it presses down as much as it presses up.

So it isn’t the air that keeps the wheel off the ground – it is the rubber tyre. What the air does is to pre-stress the rubber, so that it is in tension at every point. This holds the shape well enough to make the tyre do the work. The air, in fact, plays the same role that the spokes play in a bicycle wheel – maintaining the shape of something which is inherently flexible.

How does the air do the trick? The pressure is the same all round the wheel, so it presses down as much as it presses up.

Inflatable Bridge

Marco Peroni has invented a portable inflatable bridge, which can be erected in five hours. This is a beautiful idea: like the pneumatic tyre, it uses materials that are non-rigid to make something that is more or less rigid, and certainly very strong. The football uses the same principle, as does the inflatable boat.

The combination of two disparate materials, often using one as a matrix containing the other, is as old as bricks with straw. And all but the most primitive plants and animals use specialist materials, such as flesh and bone, tissue and chitin, to achieve strength or movement.

The Archery Bow

If you make a simple bow, using a stick and a piece of string, it is a good idea to make the string shorter than the stick, so that the stick is curved, and the string is taut, even before you fit an arrow and pull. The same is true for a real bow. Why is the pre-stressing needed? If the string is limp in the normal state, then as the arrow leaves the string, no energy is being given to it, and in fact the last few centimetres of its travel will be unproductive, because of the weak tension. By making the tension significant throughout the acceleration, we can impart far more energy to the arrow. The bow is now much harder to draw.

Where does the energy go if you draw and release with no arrow to absorb energy? It’s a bad idea to do this, because the energy has to go somewhere else.

Toughened Glass

Toughened glass is the opposite of the pneumatic tyre: it is in compression on the outside, and in tension within. It can be several times stronger than ordinary glass, and instead of breaking into sharp shards, it crumbles into small pieces with dull edges. Toughened glass is made by suddenly cooling the surface of very hot glass, and then letting the inside cool slowly. Because the surface is in compression, you might think that small scratches are not likely to spread.

This picture shows a small part of the windscreen of a car, viewed between crossed polaroid filters. The intensity of the light is modulated by the variation in strain, because the effect of the glass on the polarization varies with the properties of the material.

At the end of the page about arches you can read about some structures that are internally stressed in order to fulfil their functions.

Internal stresses can be useful, but they can also be harmful, as when unsuitable welding technique sets up unwanted forces. The page about indeterminacy discusses this.

Pre-Stressing in History

If someone said that pre-stressing not only pre-dated the 20th century, but was known to the ancient Romans, you might not believe it. But think about a masonry arch – everywhere in compression. The blocks of stone could not survive as a flat beam, but by curving the structure, and by using the weight to compress it between the abutments, the builders ensure that they are everywhere in compression, unless the arch is overloaded at some point. So where are the pre-stressing wires? There aren’t any. So what is in tension? The ground under the arch.

Stressing in Nature

Pre-stressing occurs in the natural world. The trunks and branches of trees carry internal stresses that help them to combat the external ones. If you cut a trunk into planks and re-assemble them, you will not get the same results as from the original trunk.

In a sense, the muscles of animals are analogous to the stressing wires in buildings, especially those of arthropods, which are inside the hard parts.

An artificial analogue is the Bowden cable, which allows a force to be transmitted to another place and applied in a completely different direction. The outer sleeve automatically takes up a compression which balances the tension in the inner wire. The sleeve has to be anchored at both ends, so that the wire can transmit the tension. The sleeve could be used to transmit a push, by anchoring the wire at both ends. The Bowden cable is used for the brake cables of bicycles. In some examples, sleeve is anchored to the frame, allowing the cable to pull on the brake mechanism, as in the centre-pull brake. In others, both sleeve and cable are fixed to the brake mechanism, providing a pair of forces, analogous to the push-pull circuit in electronics. What do you think are the advantages and disadvantages of the two types of brake mechanism?

If you got this far, try a superb game about bridge building – http://firingsquad.gamers.com/games/pontifex/default.asp .